elimination using addition and subtraction

5m - p = 7------(1)
7m - p = 11-----(2)

(2)-(1)
2m = 4
m = 2

->5(2) - p = 7
p = 3

So m = 2, p = 3.

First: Subtract the second equation from the first to get rid of the p in order to solve for m.
7m-p=11
-(5m-p=7)

7m-p=11
-5m+p=-7 (distributed the negative)
-------------
2m=4 (divide by 2 to get m)
m=2

Then to get p, plug m=2 back into one of the original equations and solve for p.
(I solve for both just to show you either one works)
5m-p=7 7m-p=11
5(2)-p=7 7(2)-p=11
10-p=7 14-p=11
-p=7-10 -p=11-14
-p=-3 -p=-3
p=3 p=3

Therefore, m=2 and p=3.